Compensation method for reducing intersymbol interference products caused by signal transmission via dispersive media

ABSTRACT

In accordance with the presently claimed invention, compensation for reducing ISI products within an electrical data signal corresponding to a detected data signal received via a signal transmission medium introduces distinct compensation effects for individual ISI products within the electrical data signal. Distinct data signal components within the detected data signal and corresponding to such ISI products can be selectively and individually compensated, thereby producing a compensated data signal in which each selected one of such individual data signal components is substantially removed. Individual data signal components or selected combinations of data signal components can be compensated as desired.

RELATED APPLICATIONS

[0001] This application is a continuation of U.S. patent applicationSer. No. 10/117,293, filed Apr. 5, 2002.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to signal transmission anddetection, and in particular, to techniques for compensating for signaldistortions caused by signal dispersion and nonlinearities within thesignal transmission media.

[0004] 2. Description of the Related Art

[0005] Referring to FIG. 1, a conventional fiber optic signal systemincludes a data source 10, a light source (e.g., a laser) 12, the fiberoptic medium 14, a signal detector (e.g., photodetector) 16 and anamplifier (e.g., transimpedance) 18, interconnected substantially asshown. The data source 10 provides a stream, or sequence, of datasymbols 11 which modulate the light source 12 which, in turn, launchesan optical signal 13 into the optical fiber 14. (Typically each datasymbol consists of a single data bit.) At the reception end of the fiber14, the optical signal 15 is received and detected by the detector 16,with the resultant signal 17 being amplified by the amplifier 18 toproduce the electrical data signal 19 representing the sequence of datasymbols. This signal 19 is then processed by clock and data recovery(“CDR”) circuitry (not shown) to recover the actual data and associatedclock signals.

[0006] The detector 16 is typically some form of a direct detector, suchas a photodetector. As is well known, the photodetector detects themodulated light forming the optical signal and, based on the amount ofphotonic energy in the optical signal, generates an electrical currentsignal corresponding to that photonic energy. Accordingly, the amplitudeof the electrical current signal so generated varies in linearproportion to the received optical signal power since the amplitude ofthe current is proportional to the square of the optical signalamplitude.

[0007] It is well known that the bit rate of the data signal 11, as wellas the length of the optical fiber 14, are limited in terms of howreliably a transmitted data can be received and accurately detected, dueto the non-ideal characteristics of the fiber optic transmission medium14. Referring to FIG. 2, for example, it is well known that an inputdata symbol 13, after propagating through the optical fiber 14, emergesas an optical signal 15 displaying a certain amount of signaldispersion. The amount of the signal dispersion increases in a mannercorresponding to increases in the bit rate of the data signal 11 andlength of the optical fiber 14.

[0008] One form of dispersion is chromatic dispersion which has a lineardelay versus frequency characteristic. However, with direct opticalsignal detection, such as that done when using a photodetector,chromatic dispersion causes nonlinear distortions in the electricalsignal of the receiver. Simple conventional linear equalizationtechniques are not adequate for compensating for such dispersion.

[0009] Referring to FIGS. 3A-3C, another form of dispersion is polar, orpolar mode, dispersion. As shown in FIG. 3A, an optical signaltransmitted through a single mode optical fiber actually transits lightin two distinct polarization modes 21 i, 21 q. As is well known, theelectrical fields of these two modes 21 i, 21 q are orthogonal to eachother. As the optical signal travels through the optical fiber 14, thesetwo signal modes 21 i, 21 q become misaligned, as shown in FIG. 3B. Theamount of dispersion, or distance, 23 a between these two modes 21 i, 21q is dependent upon how asymmetrical certain characteristics of theoptical fiber 14 are. For example, this dispersion 23 will increase inrelation to the degree to which the refractive indices for each of thepolarization modes 21 i, 21 q differ from each other within the opticalfiber 14.

[0010] Referring to FIG. 3C, such asymmetrical characteristics of theoptical fiber 14 tend to vary randomly along the fiber 14. Additionally,the optical signal can sometimes shift randomly between the polarizationmodes, thereby causing the phase shift between the two polarizationmodes to not accumulate consistently along the length of the opticalfiber 14. Accordingly, the pulse duration 23 b becomes stretched intime.

[0011] With polarization dispersion occurring in addition to chromaticdispersion, simple linear equalization techniques become even lesseffective as well as less practical due to the increasing complexity ofthe equalization circuitry necessary for compensation.

[0012] Referring to FIG. 4, the effect that such signal dispersioncharacteristics have upon the detected data signal can be betterunderstood. As discussed above, the data signal consists of data symbolsin the form of individual data bits. For this binary form of signal itis assumed that a binary value of unity (1) appears as a “high” signalvalue and a binary value of zero (0) appears as a “low” signal value atthe output 17 of the detector 16 (or output 19 of the amplifier 18).However, consistent with the foregoing discussion, the dispersioneffects of the optical fiber 14 are such that the value of the detectedsignal fails to achieve these ideal signal values due to the intersymbolinterference (“ISI”) caused by the dispersion effects upon adjacent databits as well as the present or desired data bit.

[0013] For example, let it be assumed that two adjacent data bits eachhave binary values of unity. Accordingly, this will produce the maximumsignal value 24. Conversely, two adjacent data bits having binary valuesof 0 will produce the minimum signal value 26. Data bit pairs of “01” or“10” will produce signal values which are somewhere between thesemaximum 24 and minimum 26 values.

[0014] For example, following a bit value of unity, the signal value 28will decrease and then either increase as value 28 a or continue todecrease as value 28 b when the value of the immediately subsequent databit is unity or zero, respectively. Similarly, following a data bitvalue of zero, the signal value 30 will increase and then eithercontinue to increase as value 30 a or decrease as value 30 b when thesubsequent data bit has a value of unity or 0, respectively.

[0015] For purposes of this example, it is further assumed that thesecond bit of this bit pair is the transmitted bit intended fordetection during the signal detection interval, centered about time Ts.By observing the signal at this time Ts, and comparing it to a thresholdTH, a decision is made as to whether the signal level indicates a bitvalue of either unity or 0. However, as seen in FIG. 4, due to thedispersion effects and resulting ISI, there is a gap 34, referred to asthe signal “eye”, between the possible signal values. As a result,incorrect decisions may be made as to the unity or zero value of thedetected signal at time Ts.

[0016] Frequently, a fixed threshold value 32 is used for making thisdecision. The problem with this conventional approach, is that if thedistortion affects cause the opening of the signal eye to not becentered about this threshold value 32 then the signal value will beincorrectly detected.

[0017] One conventional technique for compensating for this problem isto increase the effective size of the signal eye, thereby increasing thepotential distance between detected signals representing values of unityand 0. Such technique uses a feedback signal to modify, e.g., increaseor decrease as appropriate, the electrical signal 17/19 (FIG. 1) byshifting the signal wave for maximum 24 and minimum 26 levels up or downso that the effective threshold values 32 a, 32 b appear halfway betweenthem. However, while this may be effective at low data rates, it becomessignificantly less effective at high data rates.

[0018] Another conventional technique has been to modify the threshold,rather than modify the detected signal. With reference to FIG. 4, thiswould be done by shifting the threshold 32 in accordance with what theimmediately preceding adjacent data bit value was. For example, if theimmediately preceding adjacent data bit had a value of unity or zero,the effective threshold would be shifted to a higher 32 a or lower 32 bvalue, respectively.

[0019] While these techniques can be somewhat effective, such techniquesdo nothing to remove distortion from the data signal. Instead, suchtechniques merely use information about the distortion in an attempt toachieve an approximately equivalent, but inferior, effect.

[0020] Accordingly, it would be desirable to have a compensationtechnique for reducing ISI products by more directly compensating forthe individual ISI products.

SUMMARY OF THE INVENTION

[0021] In accordance with the presently claimed invention, compensationfor reducing ISI products within an electrical data signal correspondingto a detected data signal received via a signal transmission mediumintroduces distinct compensation effects for individual ISI productswithin the electrical data signal. Distinct data signal componentswithin the detected data signal and corresponding to such ISI productscan be selectively and individually compensated, thereby producing acompensated data signal in which each selected one of such individualdata signal components is substantially removed. Individual data signalcomponents or selected combinations of data signal components can becompensated as desired.

[0022] In accordance with one embodiment of the presently claimedinvention, a method for reducing intersymbol interference (ISI) productswithin a data signal includes:

[0023] receiving an input data signal that includes a first plurality ofISI products and corresponds to a detected data signal received via asignal transmission medium;

[0024] adaptively equalizing the input data signal and providing anequalized signal; and

[0025] processing the equalized signal and providing an output datasignal that includes a second plurality of ISI products which is smallerthan the first plurality of ISI products.

[0026] In accordance with another embodiment of the presently claimedinvention, a method for reducing intersymbol interference (ISI) productswithin a data signal includes:

[0027] receiving an input data signal that includes a first plurality ofISI products and corresponds to a detected data signal received via asignal transmission medium;

[0028] adaptively equalizing the input data signal and providing anequalized signal;

[0029] subtracting a processed signal from the equalized signal andproviding a resultant signal; and

[0030] processing the resultant signal and providing the processedsignal and an output data signal that includes a second plurality of ISIproducts which is smaller than the first plurality of ISI products.

[0031] In accordance with another embodiment of the presently claimedinvention, a method for reducing intersymbol interference (ISI) productswithin a data signal includes:

[0032] receiving an input data signal that includes a first plurality ofISI products and corresponds to a detected data signal received via asignal transmission medium;

[0033] adaptively equalizing the input data signal and providing a firstequalized signal;

[0034] selectively equalizing and processing the input data signal andat least a portion of the output signal and providing a processedsignal;

[0035] subtracting the processed signal from the first equalized signaland providing a resultant signal; and

[0036] processing the resultant signal and providing an output datasignal that includes a second plurality of ISI products which is smallerthan the first plurality of ISI products.

[0037] In accordance with another embodiment of the presently claimedinvention, a method for reducing intersymbol interference (ISI) productswithin a data signal includes:

[0038] receiving an input data signal that includes a first plurality ofISI products and corresponds to a detected data signal received via asignal transmission medium;

[0039] subtracting a processed signal from the input data signal andproviding a resultant signal; and

[0040] processing the resultant signal and providing the processedsignal and an output data signal that includes a second plurality of ISIproducts which is smaller than the first plurality of ISI products.

[0041] In accordance with another embodiment of the presently claimedinvention, a method for reducing intersymbol interference (ISI) productswithin a data signal includes:

[0042] receiving an input data signal that includes a first plurality ofISI products and corresponds to a detected data signal received via asignal transmission medium;

[0043] selectively equalizing and processing the input data signal andat least a portion of the output signal and providing a first processedsignal;

[0044] subtracting the first processed signal and a second processedsignal from the input data signal and providing a resultant signal; and

[0045] processing the resultant signal and providing the secondprocessed signal and an output data signal that includes a secondplurality of ISI products which is smaller than the first plurality ofISI products.

[0046] In accordance with still another embodiment of the presentlyclaimed invention, a method for reducing intersymbol interference (ISI)products within a data signal includes:

[0047] receiving an input data signal that includes a first plurality ofISI products and corresponds to a detected data signal received via asignal transmission medium;

[0048] selectively equalizing and processing the input data signal andat least a portion of the output signal and providing a processedsignal;

[0049] subtracting the processed signal from the input data signal andproviding a resultant signal; and

[0050] processing the resultant signal and providing an output datasignal that includes a second plurality of ISI products which is smallerthan the first plurality of ISI products.

[0051] In accordance with yet another embodiment of the presentlyclaimed invention, a method for reducing intersymbol interference (ISI)products within a data signal includes:

[0052] receiving an input data signal that includes a first plurality ofISI products and corresponds to a detected data signal received via asignal transmission medium;

[0053] adaptively equalizing the input data signal and providing a firstequalized signal;

[0054] selectively equalizing and processing the input data signal andat least a portion of the output signal and providing a first processedsignal;

[0055] subtracting the first processed signal and a second processedsignal from the first equalized signal and providing a resultant signal;and

[0056] processing the resultant signal and providing the secondprocessed signal and an output data signal that includes a secondplurality of ISI products which is smaller than the first plurality ofISI products.

BRIEF DESCRIPTION OF THE DRAWINGS

[0057]FIG. 1 is a functional block diagram of a conventional fiber opticsignal system.

[0058]FIG. 2 illustrates how the dispersion effects of an optical fiberproduce distortion within the optical data signal.

[0059] FIGS. 3A-3C illustrate effects of polarization mode dispersionwithin an optical fiber.

[0060]FIG. 4 illustrates relationships between detected signal valuesand signal detection thresholds.

[0061]FIG. 5 is a functional block diagram of a compensation circuit inaccordance with one embodiment of the presently claimed invention.

[0062]FIGS. 6A, 6B, 6C and 6D are functional block diagrams of examplesof adaptive signal slicers suitable for use in the circuit of FIG. 5.

[0063]FIGS. 7A and 7B are functional block diagrams of examples ofnonlinear signal processors suitable for use in the circuit of FIG. 5.

[0064]FIG. 8 is a functional block diagram of one example of afeedforward equalizer suitable for use in the circuit of FIG. 5.

DETAILED DESCRIPTION OF THE INVENTION

[0065] As an introduction to a more detailed discussion of an actualimplementation of the presently claimed invention, a discussion ispresented on the use of signal processing techniques for opticalchannels, fundamental performance limits and specific algorithmsoptimized for the optical channel with constrained architectures and/orother requirements. It begins with a simplified representation of theoptical channel with respect to signal dispersion, which is sufficientto develop an optimized algorithm design. Discussed then are performancepenalties incurred in the absence of appropriate signal processingtechniques, followed by different classes of signal processing algorithmstructures and corresponding optimized algorithms in the presence, aswell as the absence, of symbol timing information. Different adaptationalgorithm considerations are then noted. Initially, fiber and componentnonlinearities are disregarded, following which, effects and mitigationof different fiber nonlinearities and cross-talk effects are considered.

[0066] It is assumed that the data signal modulation format is thesimple but prevalent binary non-return to zero (“NRZ”), on-off keying(“OOK”) with direct detection (e.g., as opposed to multi-levelmodulation, coherent detection or sub-carrier modulated systems). Thus,the transmit signal may be expressed as follows: $\begin{matrix}{{x(t)} = {{Re}\{ {\sum\limits_{i}{a_{i}{{h_{T}( {t + {iT}} )} \cdot ^{j({{\omega_{c}t} + {\varphi_{c}{(t)}}}}}}} \}}} \\{= {{Re}\{ {\hat{x}(t)} \}}}\end{matrix}$

[0067] where h_(T)(t) represents the transmit pulse-shaping filter,{a_(i)} represents the sequence of data symbols, φ(t)=ω_(c)t+φ_(c)(t)represents the phase angle, ω_(c) represents the carrier frequency,$\frac{{\varphi_{c}(t)}}{t}$

[0068] represents the chirp (typically with direct modulators), and{circumflex over (x)}(t) is the corresponding complex signal.

[0069] Assuming only first-order polarization mode dispersion (“PMD”)and ignoring nonlinearity effects, the signal at the input of thephotodetector for the two orthogonal PMD signal modes can be expressedas follows:

s _(o,1)(t)=Re{{circumflex over (x)}(t)* (h _(c)(t)e ^(jω) ^(_(c))^(t))}+n ₁(t)=Re{S _(o,1)(t)}+n ₁(t)

s _(o,2)(t)=Re{{circumflex over (x)}(t+τ)*(h _(c)(t)e ^(jω) ^(_(c))^(t))}+n ₂(t)=Re{S _(o,2)(t)}+n ₂(t)

[0070] where h_(c)(t)→H_(c)(f)=e^(−jaf) _(²) ,$\alpha = {\pi \quad {D(\lambda)}L\frac{\lambda^{2}}{c}}$

[0071] and S_(o,1)(t), S_(o,2)(t) are the corresponding complex analyticsignals, n₁(t), n₂(t), are the Amplifier Spontaneous Emission (ASE)noise, and D(λ), L are the linear delay coefficient and fiber length,respectively. (For purposes of simplifying the analysis, the extinctionratio has been disregarded.)

[0072] The output of the photodetector (with first-order PMD effectsonly) is as follows:

s _(e)(t)=α₁(|S_(o,1)(^(t))+^(n) ₁(t)|² +α|S _(o,2)(t)|²)+n(t)

[0073] with n(t) assumed Gaussian with variance N₀/2 and accounts forthermal and shot noise.

[0074] This can be expanded to the following: $\begin{matrix}{{s_{e}(t)} = {\alpha_{1}\lbrack {{\sum\limits_{i,k}{a_{i}{{a_{k}( {{h_{T}( {t + {iT}} )}^{j\quad {\varphi_{c}{(t)}}}*{h_{c}(t)}} )} \cdot ( {{h_{T}( {t + {kT}} )}^{{- j}\quad {\varphi_{c}{(t)}}}*{h_{c}^{*}(t)}} )}}} +} }} \\{{{\alpha {\sum\limits_{i,k}{a_{i}{{a_{k}( {{h_{T}( {t + \tau + {iT}} )}^{j\quad {\varphi_{c}{({t + \tau})}}}*{h_{c}(t)}} )} \cdot ( {{h_{T}( {t + \tau + {kT}} )}^{{- j}\quad {\varphi_{c}{({t + \tau})}}}*{h_{c}^{*}(t)}} )}}}} +}} \\{{{2\alpha_{1}{{Re}\lbrack {{{S_{o,1}(t)}{n_{1}^{*}(t)}} + {\alpha \quad {S_{o,2}(t)}{n_{2}^{*}(t)}}} \rbrack}} +}} \\{{{{n_{1}(t)}}^{2} + {{n_{2}(t)}}^{2} + {n(t)}}}\end{matrix}$

[0075] For now, we will denote

N(t)=2α₁ Re[S _(o,1)(t)n ₁*(t)+αS _(o,2)(t)n ₂*(t)]+|n ₁(t)|² +|n ₂(t)|²+n(t)

[0076] which is colored noise. Generally, we will ignore the terms|n₁(t)|², n₂(t)|² in which case N(t) is Gaussian. This noise may also benon-stationary if the signal waveforms are considered to be a random (asopposed to deterministic) process.

[0077] Assuming φ_(c)(t) remains relatively constant during a dispersedsymbol time interval, this may be further simplified to: $\begin{matrix}{{s_{e}(t)} = {{\alpha_{1}{\sum\limits_{i,j}{a_{i}{a_{j}\lbrack {{{p( {t + {iT}} )}{p^{*}( {t + {jT}} )}} + {\alpha \quad {p( {t + \tau + {iT}} )}{p^{*}( {t + \tau + {jT}} )}}} \rbrack}}}} + {N(t)}}} & ( {{EQ}.\quad 1} )\end{matrix}$

[0078] or equivalently, $\begin{matrix}{{s_{e}(t)} = {{\alpha_{1}{\sum\limits_{i,j}{a_{i}{a_{j}\lbrack {{p_{i,j}(t)} + {\alpha \quad {p_{i,j}( {t + \tau} )}}} \rbrack}}}} + {N(t)}}} \\{= {{s_{e,{sig}}(t)} + {N(t)}}}\end{matrix}$

[0079] where p(t)=h_(T)(t)* h_(c)(t) (the data symbol pulse p(t) is theconvolution (“*”) of the transmit pulse-shaping filter transfer functionh_(T)(t) and the chromatic dispersion h_(c)(t)) andp_(i,j)(t)=p(t+iT)p*(t+jT).

[0080] Equation EQ. 1 is the key manifestation of dispersion (simplifiedform), which needs to be equalized or mitigated. There are two specialcases of the more general scenario set forth above, which may simplifythe analysis. The first case is where p_(i,j)(t)=0, i≠j; generallyequivalent to no chromatic dispersion, and the pulse broadening is dueto PMD and laser chirp, in which case equation EQ. 1 as set forth abovemay be simplified to the following:${s_{e}(t)} = {{\alpha_{1}{\sum\limits_{i}{a_{i}( {{p^{2}( {t + {iT}} )} + {\alpha \quad {p^{2}( {t + \tau + {iT}} )}}} )}}} + {N(t)}}$

[0081] The second case is where there is no PMD, in which case equationEQ. 1 can be simplified to:${s_{e}(t)} = {{\alpha_{1}{\sum\limits_{i,j}{a_{i}a_{j}{p( {t + {iT}} )}{p^{*}( {t + {jT}} )}}}} + {N(t)}}$

[0082] Different measures can be taken to estimate the loss due todispersion and may range from a simple computation based upon a coarseestimate to a more difficult computation based upon a more elaborateestimate. These measures can be considered in more detail as follows.

[0083] Delay spread: This is a coarse but readily computable quantity.The pulse broadening at distance z can be expressed as follows:$T_{z} = {{T_{0}\sqrt{( {1 + {\kappa \quad \beta_{2}{z/T_{0}^{2}}}} )^{2} + {( {1 + {W_{0}^{2}T_{0}^{2}}} )( {\beta_{2}{z/T_{0}^{2}}} )^{2}}}} + \tau}$

[0084] Root mean square (“RMS”) and peak distortion criteria and biterror rate (“BER”) computation: The peak distortion criterion providesthe worst case ISI distortion, which may generally occur with a very lowprobability. If a classical receiver uses a simple low-pass filter(typically matched to the transmit pulse shape) with impulse responseh_(R)(t), the signal at the output of this filter can be expressed asfollows:${{r_{e}(t)} = {{\alpha_{1}{\sum\limits_{i,j}{a_{i}{a_{j}\lbrack {{q_{i,j}(t)} + {\alpha \quad {q_{i,j}( {t + \tau} )}}} \rbrack}}}} + {n(t)}}},$

[0085] where q_(i,j)(t)=p_(i,j(t)* h) _(R)(t)

[0086] The peak distortion criterion may then be expressed as follows:$D_{p} = {\alpha_{1}E_{a}{\max_{i \in {\lbrack{0,T}\rbrack}}{\sum\limits_{{({i,j})} \neq {({0,0})}}{{{q_{i,j}(t)} + {\alpha \quad {q_{i,j}( {t + \tau} )}}}}}}}$

[0087] and for a symbol interval:${{D_{p}(t)} = {\alpha_{1}E_{a}{\sum\limits_{{({i,j})} \neq {({0,0})}}{{{q_{i,j}(t)} + {\alpha \quad {q_{i,j}( {t + \tau} )}}}}}}};{0 \leq t \leq {T.}}$

[0088] The RMS distortion criterion may also be simply computed. Withthe RMS distortion criteria, the BER may be computed assuming the ISI tobe Gaussian distributed.

[0089] BER computation with saddle-point approximation: This is a moreaccurate measure of the BER in the presence of ISI without assuming theISI to be Gaussian distributed.

[0090] Different performance bounds can be considered for purposes ofdetermining performance limits of electronic signal processing. The twomore common upper bounds of performance include the matched filter boundand the maximum likelihood sequence detection bound. When N(t)≈n(t),i.e., when ASE noise is negligible as is possible with metro systems,the matched filter bound (MFB) can be expressed as follows:${SNR}_{MFB} = \frac{\alpha_{1}^{2}E_{d}{{{p^{2}(t)} + {\alpha \quad {p^{2}( {t + \tau} )}}}}^{2}}{N_{0}/2}$

[0091] where E_(d) is the energy per data symbol.

[0092] The upper bound of the probability of bit errors can then beexpressed as follows:$P_{e} \leq {Q( \sqrt{\frac{{SNR}_{MFB}}{4}} )}$

[0093] When considering ASE noise as the dominant, noise but ignoringthe higher order powers of the ASE noise, the noise N(t) is colored andGaussian. The MFB in this case may be expressed as:${SNR}_{MFB} = \frac{\alpha_{1}^{2}E_{d}{\int_{t = 0}^{T}{( {{p^{2}(t)} + {\alpha \quad {p^{2}( {t + \tau} )}}} ){t}}}}{2N_{0}^{\prime}}$

[0094] It may be noted that, interestingly, an optimal matched filtercan be a simple “integrate and dump” type of filter.

[0095] In accordance with the presently claimed invention, nonlinearequalization in the form of decision feedback equalization (DFE) isused, and is applied based upon a rewritten form of equation EQ. 1. asfollows (where a₀ is the data symbol sought to be detected, e.g., thepresent data symbol): $\begin{matrix}{{s_{e,{stg}}(t)} = {{\alpha_{1}{a_{0}\lbrack {{p_{0,0}(t)} + {\alpha \quad {p_{0,0}( {t + \tau} )}}} \rbrack}} +}} & ({T1}) \\{\quad {{\alpha_{1}{\sum\limits_{{i \geq 0},{j > 0}}^{\quad}\quad {a_{i}{a_{j}\lbrack {{p_{i,j}(t)} + {\alpha \quad {p_{i,j}( {t + \tau} )}}} \rbrack}}}} +}} & ({T2}) \\{\quad {{\alpha_{1}a_{0}{\sum\limits_{j < 0}{a_{j}\lbrack {{p_{0,j}(t)} + {\alpha \quad {p_{0,j}( {t + \tau} )}}} \rbrack}}} +}} & ({T3}) \\{\quad {{\alpha_{1}{\sum\limits_{{i < 0},{j < 0}}^{\quad}\quad {a_{i}{a_{j}\lbrack {{p_{i,j}(t)} + {\alpha \quad {p_{i,j}( {t + \tau} )}}} \rbrack}}}} +}} & ({T4}) \\{\quad {2\alpha_{1}{\sum\limits_{{i > 0},{j < 0}}^{\quad}\quad {a_{i}{a_{j}\lbrack {{p_{i,j}(t)} + {\alpha \quad {p_{i,j}( {t + \tau} )}}} \rbrack}}}}} & ({T5})\end{matrix}$

[0096] Note that while the non-white, or colored, characteristic of theadditive noise N(t) is not considered explicitly, it may be assumed thatthe application of a linear filter whitens the noise and is subsumedwithin s_(e,sig)(t).

[0097] Referring to FIG. 5, a compensation circuit for reducingintersymbol inference products within an electrical data signalcorresponding to a detected optical data signal received via an opticalfiber in accordance with one embodiment of the presently claimedinvention includes, in various combinations as will be discussed below:an adaptive equalizer 110; a signal combiner 112; another adaptiveequalizer 114; a signal slicer 116; a nonlinear signal processor 118;another nonlinear signal processor 120; and another signal slicer 122;all interconnected substantially as shown. The electrical data signal101, corresponding to the detected optical data signal, generally in theform of a voltage signal generated by a transimpedance amplifier (notshown) from the electrical current signal produced by the photodetector,contains a sequence of data symbols. Such data symbol sequence includesa present data symbol, a sequence of past data symbols and a sequence offuture data symbols. The present data symbol is that which is sought tobe detected correctly at any given point in time, while the past datasymbols are those which have preceded the present data symbol, and thefuture data symbols are those which will follow the present data symbol.This electrical data signal 101 is processed by the first adaptiveequalizer 110 in accordance with well known adaptive equalizationtechniques. The resulting adaptively equalized signal 111 is provided tothe signal combining circuit 112. The equalization provided by thisadaptive equalizer 110 substantially removes data signal component T2representing the ISI product of the future data symbol sequence asdefined above.

[0098] The electrical data signal 101 is also adaptively equalized bythe other adaptive equalizer 114 in accordance with well known adaptiveequalization techniques. That resulting equalized signal 115 isprocessed, e.g., detected, in the signal slicer 116. The resultingsliced signal 117 corresponds to the ISI products of the future datasymbol sequence portion (“i>0”) of data signal component T5 as definedabove, and is provided to the nonlinear signal processor 118. (Thisslicing, or thresholding, function has the effect of causing this signal117 to represent tentative decisions as to the expected values of futuredata symbols within the sequence of data symbols of the electrical datasignal 101.)

[0099] The nonlinear signal processor 118 (discussed in more detailbelow) processes this sliced signal 117 together with another slicedsignal 123 (discussed in more detail below) which represents the ISIproduct of the past data symbol sequence portion (“j<0”) of data signalcomponent T5 as defined above. The resulting processed signal 119,therefore, approximately duplicates data signal component T5representing the ISI products of the past and future data symbolsequences as defined above, and is provided to the signal combiningcircuit 112.

[0100] Another nonlinear signal processor 120 also processes this secondsliced signal 123 to produce a processed signal 121 in which data signalcomponent T4 representing the ISI product of the past data symbolsequence as defined above is approximately duplicated. This signal 121is also provided to the signal combining circuit 112.

[0101] The signal combining circuit 112 combines its input signals 111,119, 121 by subtracting from the first adaptively equalized signal 111the first nonlinearly processed signal 119 and the second nonlinearlyprocessed signal 121. The resultant signal 113, therefore, has had datasignal components T2, T4, and T5 substantially removed, thereby leavingonly the desired data signal component T1 (i.e., the present, or desireddata symbol) and data signal component T3 which represents the ISIproduct of the past data symbol sequence.

[0102] The second signal slicer 122 slices this signal 113, therebysubstantially removing data signal component T3, to produce the secondsliced signal 123. In accordance with a preferred embodiment of thepresently claimed invention, the output signal slicer 122 is an adaptivesignal slicer in which the sliced output signal 123 is fed back forpurposes of adaptively modifying the threshold used within the signalslicer 122. This adaptive threshold function can be achieved inaccordance with any of a number of conventional techniques and isdiscussed in more detail below.

[0103] Alternatively, and in more specific detail, the operation of thecircuitry of FIG. 5 can be described as follows. To compensate thepre-cursor ISI term T2, a linear, pre-cursor equalizer in the form ofadaptive equalizer 110 is used. This filter is preferably a feedforwardtransversal filter. For example, adaptive equalizer 110 can be asymbol-spaced transversal filter with the following impulse response:${h_{B}(t)} = {\sum\limits_{k = {- M}}^{M}\quad {d_{k}{\delta ( {t - {k\quad T}} )}}}$

[0104] The criterion for selecting the precise filter h_(B)(t) so as tomaximize its response is as follows: $\begin{matrix}{\rho = \frac{ {\lbrack {{p_{0,0}(t)} + {\alpha \quad {p_{0,0}( {t + \tau} )}}} )*{h_{B}(t)}} \rbrack^{2}}{\sum\limits_{{i \geq 0},{j > 0}}^{\quad}( {\lbrack {{p_{i,j}(t)} + {\alpha \quad {p_{i,j}( {t + \tau} )}}} \rbrack*{h_{B}(t)}} )^{2}}} \\{= \frac{( {{\overset{\_}{P}}^{\{{0,0}\}}\underset{\_}{d}} )^{2}}{\sum\limits_{{i \geq 0},{j > 0}}^{\quad}( {{\overset{\_}{P}}^{\{{i,j}\}}\underset{\_}{d}} )^{2}}}\end{matrix}$

[0105] The ISI term T5 is compensated by a combination of differentfilter structures. This includes a nonlinear processor 118, whichproduces a scaled sum based on the designed weighting coefficients ofthe filter${h_{C}(t)} = {\sum\limits_{k}{f_{k}{\delta ( {t - {k\quad T}} )}}}$

[0106] of products of symbols. The output of the nonlinear processor 118is a sequence of the following form:$\sum\limits_{{i > 0},{j < 0}}^{\quad}{f_{({i,j})}\quad {\overset{\bigwedge}{a}}_{i}{{\overset{\bigwedge}{a}}_{j}.}}$

[0107] Estimates of the past symbols {â_(j)}_(j<0) are obtained from theoutput signal slicer 122, which serves as a Final Decision block, whileestimates of the future symbols {â_(i)}_(1>0) are obtained from theother signal slicer 116, which serves as a Tentative Decision block.This Tentative Decision block can be a simple two-level slicer. Due tothe possibility of error propagation as the decisions are onlytentative, improved performance may be expected using a three-levelslicer with the middle level indicating an erasure or no-decision.

[0108] The associated adaptive equalizer 114 is preferably adaptive andfractionally-spaced, but can also be fixed and symbol-spaced as well inwhich case this filter 114 is of the form${h_{A}(t)} = {\sum\limits_{k}^{\quad}\quad {g_{k}{{\delta ( {t - {kT}} )}.}}}$

[0109] This filter, or bank of filters, together with the slicer 116predicts the future symbols. Thus, a simple design for h_(A)(t) is abank of filters such that the filters are matched to{p_(k,k)(t)+αp_(k,k)(t+τ)}_(k>0) for nearly maximizing thesignal-to-noise ratio (“SNR”) for the future symbols.

[0110] The ISI term T3 which also contains the desired symbol, albeitscaled by past symbols, is compensated by the output signal slicer 122,which preferably includes a two-level slicer and can also contain afinite impulse response (“FIR”) filter with appropriate weightings ofpast symbols. The output of such a FIR filter is used to approximate thefollowing term:$\sum\limits_{j < 0}^{\quad}\quad {a_{j}\lbrack {{p_{0,j}(t)} + {\alpha \quad {p_{0,j}( {t + \tau} )}}} \rbrack}$

[0111] It should be noted that the threshold in this slicer 122 can beadapted based on a table as a function of past decisions that have beenmade. Such table can have up to 2^(M) entries where M is the length ofthe post-cursor ISI in number of symbols.

[0112] The ISI term T4 is compensated using another nonlinear processor120, which produces a scaled sum based on the designed weightingcoefficients of the filter${h_{D}(t)} = {\sum\limits_{k}^{\quad}\quad {h_{k}{\delta ( {t - {kT}} )}}}$

[0113] of products of symbols. The output of this nonlinear processor120 is a sequence of the following form:$\sum\limits_{{i < 0},{j < 0}}^{\quad}\quad {h_{({i,\quad j})}{\hat{a}}_{i}\quad {{\hat{a}}_{j}.}}$

[0114] Estimates of past symbols {â_(j)}^(j<0) are obtained from theFinal Decision block 122.

[0115] The weighting coefficients for the adaptive equalizers 110, 114as well as the weighting coefficients for the nonlinear filters 118, 120can be designed with least-mean square (“LMS”) or zero-forcing criteria.

[0116] Consistent with the principles of the present invention, itshould be appreciated that the data signal component-specific nature ofthe compensation provided, as discussed above, need not necessarily beperformed upon all four of the undesired data signal components (T2, T3,T4 and T5). For example, compensation can be limited or appliedprimarily to the following individual data signal components orcombinations of data signal components as follows (with no significanceattached to the order in which they are listed): signal components T2and T3; signal components T2, T3 and T4; signal components T2, T3 andT5; signal components T2 and T4; signal components T2, T4 and T5; andsignal components T2 and T5. Similarly, compensation can be limited orapplied primarily as follows: signal components T3 and T4; signalcomponents T3, T4 and T5; and signal components T3 and T5. Furthersimilarly, compensation can be limited or applied primarily as follows:signal component T4; signal components T4 and T5; and signal componentT5.

[0117] In those cases in which fewer than all four undesired data signalcomponents are compensated, based upon the foregoing discussion and thecircuit of FIG. 5, it should be understood that the circuit connectionswould be modified as follows. Where no compensation is to be providedfor data signal component T2, the first adaptive equalizer 110 is notused or is bypassed and the electrical data signal 101 is provideddirectly to the “positive” input terminal of the signal combiningcircuit 112. Where no compensation for data signal component T3 is to beprovided, the second signal slicer 122 is a fixed-threshold signalslicer instead of an adaptive signal slicer (discussed in more detailbelow).

[0118] Where no compensation for data signal component T4 is to beprovided, the second nonlinear signal processor 120 is not used and noconnection is made to the corresponding “negative” input to the signalcombining circuit 112. Similarly, where no compensation for data signalcomponent T5 is to be provided, the second adaptive equalizer 114, thefirst signal slicer 116 and first nonlinear signal processor 118 are notused and no connection is made to the corresponding “negative” input tothe signal combining circuit 112.

[0119] Based upon the foregoing discussion, a number of principles,characteristics and features of the present invention should be evident.First, the beneficial data signal compensation provided in accordancewith the present invention is not limited to electrical data signalsdetected from optical data signals. Indeed, such compensation techniquescan be applied to any electrical data signal corresponding to a detecteddata signal received via a signal transmission medium, with an opticalmedium merely being one example.

[0120] Second, the signal model used for purposes of determining howbest to apply compensation to the various components of the data signalis not limited to that presented above. The signal model discussed abovehas been presented as an example for purposes of illustrating the moregeneral feature of the present invention, i.e., selective application ofcompensation to individual, discrete data signal components.

[0121] For example, the topology, or architecture, of the circuit andfunctions as depicted in FIG. 5 advantageously allows compensation to beselectively applied to individual, discrete data signal components byperforming four major functions. The circuit branch containing the firstadaptive equalizer 110 processes the electrical data signal 101 in sucha manner as to substantially remove one distinct signal componentrepresenting an ISI product of some portion of the data symbol sequence(e.g., a portion of the future data symbol sequence, as discussed forthe example above). The circuit branch containing equalization andprocessing circuitry in the form of the other adaptive equalizer 114,signal slicer 116 and nonlinear signal processor 118 approximatelyduplicates an ISI product of another portion of the data symbol sequence(e.g., portions of the past and future data symbol sequences, asdiscussed for the example above) for removal by subtraction within thesignal combiner 112 from the compensated signal 111 provided by thefirst adaptive equalizer 110. The circuit branch containing outputprocessing circuitry in the form of the other signal slicer 122 andnonlinear signal processor 120 approximately duplicates an ISI productof still another portion of the data symbol sequence (e.g., anotherportion of the past data symbol sequence, as discussed for the exampleabove) for removal by subtraction within the signal combiner 112 fromthe compensated signal 111 provided by the first adaptive equalizer 110.

[0122] Referring to FIG. 6A, one example of an adaptive signal slicer122 a suitable for use in the circuit of FIG. 5 has a slicing, orthreshold, circuit 210 having a threshold which is controlled orprovided by a threshold control signal 213 from a threshold valuecircuit 212. The sliced data 211 is provided to a shift register 214,the contents 123 a of which are used to determine the threshold controlsignal 213 provided by the threshold value circuit 212. In oneembodiment, this threshold value circuit 212 can be a memory circuit,such as a random access memory or lookup table, which uses the shiftregister output 123 a as an address signal for selecting the appropriateoutput 213 for use as the threshold data or control signal.

[0123] Referring to FIG. 6B, another example of an adaptive signalslicer 122 b suitable for use in the circuit of FIG. 5 has a signalsumming, or scaling, stage 210 a in which the incoming signal 113 issummed, or scaled in accordance, with the threshold control signal 213from the threshold value circuit 212. The scaled signal 215 is sliced bythe slicing, or threshold, circuit 210 b using a fixed threshold. Asbefore, the sliced data 211 is provided to a shift register 214, thecontents 123 a of which are used to determine the threshold controlsignal 213 provided by the threshold value circuit 212. (Alternatively,in place of the scaling stage 210 a, threshold control signal 213 andthreshold value circuit 212, a variable gain stage, gain control signaland gain control circuit, respectively (not shown), can be used, wherebythe variable gain stage would amplify or attenuate the incoming signal113 in accordance with the gain control signal provided by the gaincontrol circuit.) Referring to FIG. 6C, still another example of anadaptive signal slicer 122 c suitable for use in the circuit of FIG. 5has a multiple-level (e.g., m levels) slicer 210 c in which the incomingsignal is compared against m thresholds V1, V2, V3, . . . , Vm, with oneof the m sliced signals 217 a, 217 b, . . . , 217 m selected by amultiplexor 210 d. The output 123 c of the multiplexor 210 d issequentially delayed by a number of delay elements 212 a (e.g., a shiftregister), with the resultant delayed signals 219 a, 219 b, . . . , 219n used to address a memory element (e.g., a lookup table) 212 b, theoutput 213 a of which controls the multiplexor 210 d.

[0124] Referring to FIG. 6D, yet another example of an adaptive signalslicer 122 d suitable for use in the circuit of FIG. 5 also has themultiple-level slicer 210 c and multiplexor 210 d. In this circuit 122d, the delay elements 212 a in cooperation with a nonlinear processor212 c use the delayed signals 219 a, 219 b, . . . , 219 n to produce asum of products, the result 213 b of which controls the multiplexor 210d.

[0125] Referring to FIG. 7A, one example of a nonlinear signalprocessing circuit 118 a/120 a suitable for use as the nonlinear signalprocessors 118, 120 in the circuit of FIG. 5 includes a number ofmultiplier circuits 224 for generating the signal products 225 withindata signal components T4 and T5, and a summing circuit 226 for summingsuch signal products 225. The respective sliced data signal components123 are multiplied together, along with corresponding scaling data 223,in accordance with the ISI equation set forth above.

[0126] Referring to FIG. 7B, another example of a nonlinear signalprocessing circuit 118 b/120 b suitable for use as the nonlinear signalprocessors 118, 120 in the circuit of FIG. 5 also includes a number ofmultiplier circuits 304 for generating signal products 305 bymultiplying time-delayed versions 303 of the input signal 301 (delayedby delay elements 302), and a summing circuit 306 for summing suchsignal products 305.

[0127] Referring to FIG. 8, an adaptive equalizer circuit 110 a/114 asuitable for use as the adaptive equalizers 110, 114 in the circuit ofFIG. 5 can be a conventional feedforward equalizer as shown. Preferably,it is a fractionally-spaced transversal equalizer in which each of therespective time delay intervals Td is less than the period of one datasymbol. In accordance with well known techniques, the incoming datasignal 101 is progressively delayed by time delay elements 240. Thetapped signals 101, 241 are individually multiplied by respectiveequalizer coefficients 243 within the multipliers 242. The resultingsignals 243 are then summed in a summer 244, with the summed signal 245sliced by a signal slicer 246 to produce the equalized output signal111/115 (FIG. 5).

[0128] As will be readily understood by those of ordinary skill in theart, the individual circuit elements and functions discussed herein arewell known and understood, and can be readily constructed and practicedin numerous ways using either analog or digital implementations as wellas combinations of both. For example, analog implementations of thenonlinear signal processing circuit 118 a/120 a of FIG. 7 or adaptiveequalizer circuit 110 a/114 a of FIG. 8 could use well known Gilbertcell circuitry for the multipliers 224, 242, simple voltage summingcircuitry for the adders 226, 244, and passive filters (withsubstantially constant group delay) for the delay elements 240. Digitalimplementations of these circuits 118 a/120 a, 110 a/114 a could usewell known combinations of binary registers and counters for themultipliers 224, 242, combinations of binary logic circuits for theadders 226, 244, and binary shift registers or flip flops for the delayelements 240.

[0129] As will be further understood, while the present invention hasbeen discussed in the context of implementations using discreteelectronic circuitry (preferably in the form of one or more integratedcircuit chips), the functions of any part of such circuitry may beimplemented using one or more appropriately programmed processors,depending upon the data symbol rates to be processed.

[0130] As will be still further understood, while the present inventionhas been discussed in the context of the detection of signals receivedvia signal transmission media in the form of optical fiber, thecompensation principles and techniques discussed herein are alsoapplicable to and useful for the detection of signals received via otherforms of dispersive media.

[0131] Various other modifications and alterations in the structure andmethod of operation of this invention will be apparent to those skilledin the art without departing from the scope and spirit of the invention.Although the invention has been described in connection with specificpreferred embodiments, it should be understood that the invention asclaimed should not be unduly limited to such specific embodiments. It isintended that the following claims define the scope of the presentinvention and that structures and methods within the scope of theseclaims and their equivalents be covered thereby.

What is claimed is:
 1. A method for reducing intersymbol interference(ISI) products within a data signal, comprising: receiving an input datasignal that includes a first plurality of ISI products and correspondsto a detected data signal received via a signal transmission medium;adaptively equalizing said input data signal and providing an equalizedsignal; and processing said equalized signal and providing an outputdata signal that includes a second plurality of ISI products which issmaller than said first plurality of ISI products.
 2. The method ofclaim 1, wherein said adaptively equalizing said input data signal andproviding an equalized signal comprises linearly equalizing said inputdata signal.
 3. The method of claim 1, wherein said processing saidequalized signal and providing an output data signal that includes asecond plurality of ISI products which is smaller than said firstplurality of ISI products comprises slicing said resultant signal andproviding a sliced signal as said output signal.
 4. The method of claim3, wherein said slicing said resultant signal and providing a slicedsignal as said output signal comprises adaptively slicing said resultantsignal.
 5. A method for reducing intersymbol interference (ISI) productswithin a data signal, comprising: receiving an input data signal thatincludes a first plurality of ISI products and corresponds to a detecteddata signal received via a signal transmission medium; adaptivelyequalizing said input data signal and providing an equalized signal;subtracting a processed signal from said equalized signal and providinga resultant signal; and processing said resultant signal and providingsaid processed signal and an output data signal that includes a secondplurality of ISI products which is smaller than said first plurality ofISI products.
 6. The method of claim 5, wherein said adaptivelyequalizing said input data signal and providing an equalized signalcomprises linearly equalizing said input data signal.
 7. The method ofclaim 5, wherein said processing said resultant signal and providingsaid processed signal and an output data signal that includes a secondplurality of ISI products which is smaller than said first plurality ofISI products comprises: slicing said resultant signal and providing asliced signal as said output signal; and nonlinearly processing at leasta portion of said sliced signal and providing said processed signal. 8.The method of claim 7, wherein said slicing said resultant signal andproviding a sliced signal as said output signal comprises adaptivelyslicing said resultant signal.
 9. The method of claim 8, wherein saidadaptively equalizing said input data signal and providing an equalizedsignal comprises linearly equalizing said input data signal.
 10. Amethod for reducing intersymbol interference (ISI) products within adata signal, comprising: receiving an input data signal that includes afirst plurality of ISI products and corresponds to a detected datasignal received via a signal transmission medium; adaptively equalizingsaid input data signal and providing a first equalized signal;selectively equalizing and processing said input data signal and atleast a portion of said output signal and providing a processed signal;subtracting said processed signal from said first equalized signal andproviding a resultant signal; and processing said resultant signal andproviding an output data signal that includes a second plurality of ISIproducts which is smaller than said first plurality of ISI products. 11.The method of claim 10, wherein said adaptively equalizing said inputdata signal and providing a first equalized signal comprises linearlyequalizing said input data signal.
 12. The method of claim 10, whereinsaid selectively equalizing and processing said input data signal and atleast a portion of said output signal and providing a processed signalcomprises: adaptively equalizing said input data signal and providing asecond equalized signal; slicing said second equalized signal andproviding a sliced signal; and nonlinearly processing said sliced signaland said at least a portion of said output signal and providing saidprocessed signal.
 13. The method of claim 12, wherein said adaptivelyequalizing said input data signal and providing a second equalizedsignal comprises linearly equalizing said input data signal.
 14. Themethod of claim 10, wherein said processing said resultant signal andproviding an output data signal that includes a second plurality of ISIproducts which is smaller than said first plurality of ISI productscomprises slicing said resultant signal and providing a sliced signal assaid output signal.
 15. The method of claim 14, wherein said slicingsaid resultant signal and providing a sliced signal as said outputsignal comprises adaptively slicing said resultant signal.
 16. Themethod of claim 15, wherein said adaptively equalizing said input datasignal and providing a first equalized signal comprises linearlyequalizing said input data signal.
 17. The method of claim 15, whereinsaid selectively equalizing and processing said input data signal and atleast a portion of said output signal and providing a processed signalcomprises: adaptively equalizing said input data signal and providing asecond equalized signal; slicing said second equalized signal andproviding a sliced signal; and nonlinearly processing said sliced signaland said at least a portion of said output signal and providing saidprocessed signal.
 18. The method of claim 17, wherein said adaptivelyequalizing said input data signal and providing a second equalizedsignal comprises linearly equalizing said input data signal.
 19. Amethod for reducing intersymbol interference (ISI) products within adata signal, comprising: receiving an input data signal that includes afirst plurality of ISI products and corresponds to a detected datasignal received via a signal transmission medium; subtracting aprocessed signal from said input data signal and providing a resultantsignal; and processing said resultant signal and providing saidprocessed signal and an output data signal that includes a secondplurality of ISI products which is smaller than said first plurality ofISI products.
 20. The method of claim 19, wherein said processing saidresultant signal and providing said processed signal and an output datasignal that includes a second plurality of ISI products which is smallerthan said first plurality of ISI products comprises: slicing saidresultant signal and providing a sliced signal as said output signal;and nonlinearly processing at least a portion of said sliced signal andproviding said processed signal.
 21. The method of claim 20, whereinsaid slicing said resultant signal and providing a sliced signal as saidoutput signal comprises adaptively slicing said resultant signal.
 22. Amethod for reducing intersymbol interference (ISI) products within adata signal, comprising: receiving an input data signal that includes afirst plurality of ISI products and corresponds to a detected datasignal received via a signal transmission medium; selectively equalizingand processing said input data signal and at least a portion of saidoutput signal and providing a first processed signal; subtracting saidfirst processed signal and a second processed signal from said inputdata signal and providing a resultant signal; and processing saidresultant signal and providing said second processed signal and anoutput data signal that includes a second plurality of ISI productswhich is smaller than said first plurality of ISI products.
 23. Themethod of claim 22, wherein said selectively equalizing and processingsaid input data signal and at least a portion of said output signal andproviding a first processed signal comprises: adaptively equalizing saidinput data signal and providing an equalized signal; slicing saidequalized signal and providing a sliced signal; and nonlinearlyprocessing said sliced signal and said at least a portion of said outputsignal and providing said first processed signal.
 24. The method ofclaim 23, wherein said adaptively equalizing said input data signal andproviding an equalized signal comprises linearly equalizing said inputdata signal.
 25. The method of claim 22, wherein said processing saidresultant signal and providing said second processed signal and anoutput data signal that includes a second plurality of ISI productswhich is smaller than said first plurality of ISI products comprises:slicing said resultant signal and providing a sliced signal as saidoutput signal; and nonlinearly processing at least a portion of saidsliced signal and providing said second processed signal.
 26. The methodof claim 25, wherein said slicing said resultant signal and providing asliced signal as said output signal comprises adaptively slicing saidresultant signal.
 27. The method of claim 26, wherein said selectivelyequalizing and processing said input data signal and at least a portionof said output signal and providing a first processed signal comprises:adaptively equalizing said input data signal and providing an equalizedsignal; slicing said equalized signal and providing a sliced signal; andnonlinearly processing said sliced signal and said at least a portion ofsaid output signal and providing said first processed signal.
 28. Themethod of claim 27, wherein said adaptively equalizing said input datasignal and providing an equalized signal comprises linearly equalizingsaid input data signal.
 29. A method for reducing intersymbolinterference (ISI) products within a data signal, comprising: receivingan input data signal that includes a first plurality of ISI products andcorresponds to a detected data signal received via a signal transmissionmedium; selectively equalizing and processing said input data signal andat least a portion of said output signal and providing a processedsignal; subtracting said processed signal from said input data signaland providing a resultant signal; and processing said resultant signaland providing an output data signal that includes a second plurality ofISI products which is smaller than said first plurality of ISI products.30. The method of claim 29, wherein said selectively equalizing andprocessing said input data signal and at least a portion of said outputsignal and providing a processed signal comprises: adaptively equalizingsaid input data signal and providing an equalized signal; slicing saidequalized signal and providing a sliced signal; and nonlinearlyprocessing said sliced signal and said at least a portion of said outputsignal and providing said processed signal.
 31. The method of claim 30,wherein said adaptively equalizing said input data signal and providingan equalized signal comprises linearly equalizing said input datasignal.
 32. The method of claim 29, wherein said processing saidresultant signal and providing an output data signal that includes asecond plurality of ISI products which is smaller than said firstplurality of ISI products comprises slicing said resultant signal andproviding a sliced signal as said output signal.
 33. The method of claim32, wherein said slicing said resultant signal and providing a slicedsignal as said output signal comprises adaptively slicing said resultantsignal.
 34. The method of claim 33, wherein said selectively equalizingand processing said input data signal and at least a portion of saidoutput signal and providing a processed signal comprises: adaptivelyequalizing said input data signal and providing an equalized signal;slicing said equalized signal and providing a sliced signal; andnonlinearly processing said sliced signal and said at least a portion ofsaid output signal and providing said processed signal.
 35. The methodof claim 34, wherein said adaptively equalizing said input data signaland providing an equalized signal comprises linearly equalizing saidinput data signal.
 36. A method for reducing intersymbol interference(ISI) products within a data signal, comprising: receiving an input datasignal that includes a first plurality of ISI products and correspondsto a detected data signal received via a signal transmission medium;adaptively equalizing said input data signal and providing a firstequalized signal; selectively equalizing and processing said input datasignal and at least a portion of said output signal and providing afirst processed signal; subtracting said first processed signal and asecond processed signal from said first equalized signal and providing aresultant signal; and processing said resultant signal and providingsaid second processed signal and an output data signal that includes asecond plurality of ISI products which is smaller than said firstplurality of ISI products.
 37. The method of claim 36, wherein saidadaptively equalizing said input data signal and providing a firstequalized signal comprises linearly equalizing said input data signal.38. The method of claim 36, wherein said selectively equalizing andprocessing said input data signal and at least a portion of said outputsignal and providing a first processed signal comprises: adaptivelyequalizing said input data signal and providing a second equalizedsignal; slicing said second equalized signal and providing a slicedsignal; and nonlinearly processing said sliced signal and said at leasta portion of said output signal and providing said first processedsignal.
 39. The method of claim 38, wherein said adaptively equalizingsaid input data signal and providing a second equalized signal compriseslinearly equalizing said input data signal.
 40. The method of claim 36,wherein said processing said resultant signal and providing said secondprocessed signal and an output data signal that includes a secondplurality of ISI products which is smaller than said first plurality ofISI products comprises: slicing said resultant signal and providing asliced signal as said output signal; and nonlinearly processing at leasta portion of said sliced signal and providing said second processedsignal.
 41. The method of claim 40, wherein said slicing said resultantsignal and providing a sliced signal as said output signal comprisesadaptively slicing said resultant signal.
 42. The method of claim 41,wherein said adaptively equalizing said input data signal and providinga first equalized signal comprises linearly equalizing said input datasignal.
 43. The method of claim 41, wherein said selectively equalizingand processing said input data signal and at least a portion of saidoutput signal and providing a first processed signal comprises:adaptively equalizing said input data signal and providing a secondequalized signal; slicing said second equalized signal and providing asliced signal; and nonlinearly processing said sliced signal and said atleast a portion of said output signal and providing said first processedsignal.
 44. The method of claim 43, wherein said adaptively equalizingsaid input data signal and providing a second equalized signal compriseslinearly equalizing said input data signal.